The effect of asymmetric laser pulses on electron yield from a laser wakefield accelerator has been experimentally studied using > 10^19 cm^-3 plasmas and a 10 TW, > 45 fs, Ti:Al_2O_3 laser. Laser pulse shape was controlled through non-linear chirp with a grating pair compressor. Pulses (76 fs FWHM) with a steep rise and positive chirp were found to significantly enhance the electron yield compared to pulses with a gentle rise and negative chirp. Theory and simulation show that fast rising pulses can generate larger amplitude wakes that seed the growth of the self-modulation instability and that frequency chirp is of minimal importance for the experimental parameters.